Question

An LTI system has an impulse answer of h[n] = a^(n)H[n], H[n] is the Heaviside step function. Obtain the output y[n] from the system when the input is x[n]=H[n]. 2. Consider the discrete system defined by> y[n] - ay[n-1] =x[n] Find the output when the input is x[n] = Kb^(n)H[n], and y[-1]=y_(-1)\ Find the output when the input is x[n] = K ẟ [n], and y[-1]=a Find the impulse response when the system is initially at rest. Find the Heaviside step response when the system is initially at rest.

Answer #1

An LTI discrete-time system has the impulse response h[n] =
(1.2)^n * u[-n]. Find the system response to a unit step input x[n]
= u[n].
Please explain the shifting im having a hard time grasping the
concept (especially for the U[-n+k] shift
Note:u[n] is the unit step function

The signal x[n] is the input of an LTI system with impulse
function of h[n]. x[n] = (0.4)^n u[n] and h[n] = (0.2)^n u[n].
(a) What is the DTFT of the output of the LTI system?
(b) What are the Energy density spectrums of the input and
output signals?
(c) What would be the inverse DTFT: X(w) =
1/(1-0.25e^-j(w-2))
(d) How would part (c) differ for the DTFT: X(w) =
1/(1-0.25e^-j(w-2)) + 1/(1-0.25e^-j(w+2))

The impulse response of an LTI system is h[n] = 3u[n+2]. a) Is
this system BIBO stable? Justify. b) Is the system causal?
Justify.

For the LTI system described by the following system functions,
determine (i) the impulse response (ii) the difference equation
representation (iii) the pole-zero plot, and (iv) the steady state
output y(n) if the input is x[n] = 3cos(πn/3)u[n].
a. H(z) = (z+1)/(z-0.5), causal system (Hint: you need to
express H(z) in z-1 to find the difference equation )
b. H(z) = (1 + z-1+ z-2)/(1-1.7z-1+0.6z-2), stable system
c. Is the system given in (a) stable? Is the system given in...

Consider a causal LTI system described by the difference
equation:
y[n] = 0.5 y[n-1] + x[n] – x[n-1]
(a) Determine the system function H(z) and plot a pole-zero pattern
in the complex z-plane.
(b) Find the system response using partial fraction expansion when
the input is x[n] = 2u[n]. Plot the result.

Solve this signal problem.
Suppose the output y[n] of a DT LTI system with input x[n] is
y[n-1] - 10/3y[n] + y[n+1] = x[n]
The system is stable and the impulse response of h[n] =
A1*(B1)^n*C1 + A2*(B2)^n*C2 is then,
What is A1?
What is B1?
What is C1?
What is A2?
What is B2?
What is C2?

(d) A test on unknown LTI system is conducted by given an
impulse as the input. The output impulse response from this test is
given by:
ℎ[?]=[?[?−1]−?[?−4]]?[?]
A signal ?[?]=4?[?−1]+14[?[?]−?[?−3]] will be the new input to that
system. Find the new output if the input-output relationship for a
system given as ?[?]=ℎ[?]∗?[?].
[10 marks]

CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY
MAHMOOD NAHVI
11. In an LTI system, x(n) is the input and h(n) is the
unit-sample response. Find and sketch the
output y(n) for the following cases:
i) x(n) = 0.3nu(n) and h(n) = 0.4nu(n)
ii) x(n) = 0.5nu(n) and h(n) = 0.6nu(n)
iii) x(n) = 0.5|n|u(n) and h(n) = 0.6nu(n)

For an LTI system h[n], the output is given by
y[n] = 2δ[n-1],
given that
x[n] = δ[n]-2δ[n-1]+ 2δ[n-2].
a) Find the transfer function H(z) (7 Points).
b) Find the difference equation of the overall system (8
Points).
c) Given that the system is causal find h[n] (10 Points).
d) Given that the system does not have Fourier Transform, find h[n]
(10 Points).

a) If the transfer function of a system is H(z) = 2+z^(-2), what
is its impulse response?
b) If the transfer function of a system is 2z/(z-0.5) and it is
valid for when |z| > 0.5, what is its impulse response?
c) If the transfer function of a system is 1/(z-2), what is its
impulse response?
d) x[n] = (-4)^n U[n]. (U[n] is the unit step function). What is
its z-transform and the region of convergence of its
z-transform?
e)...

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